The biggest factor is 'Betz', the guy that figured out that a windmill has a theoretical upper limit of efficiency of ~59%, the easiest explanation for that is that in order for the windmill to work you have to slow down the moving air but the air should still be able to escape to allow the cycle to continue.
The practical upshot of that is that you can't slow the air down to a standstill, and hence you can only extract so much power.
The next step is the difference between the theoretical maximum and the actual rotor used to extract the energy, this will always be a compromise, but real world rotor efficiencies of about 50% can be reached. Then there's the generator/alternator (depending on the type of machine) losses and gearbox losses if a gearbox is used (there are very large direct drive models, specifically the Enercon series).
After all is said and done figure about 35 to 48% of the wind 'input' energy can be extracted and applied to do something useful, assuming the wind is blowing at 'rated speed' (when the machine produces its maximum design power).
If the wind goes over that speed you will lose power because the blades will be 'furled' to take them out of the wind to limit the rotor speed to something safe, and to avoid burning up the powertrain or wrecking the gearbox.
Then there are still transmission losses but we can leave those out because they apply to any power source connected to the grid.
Typical rotor diameters for 2MW machines are in the 80 to 90 meter range depending on how efficient the machine is.
There is no 'typical wind farm', it all depends on the effects of the terrain and the windmills on each other and the amount of investment.
A single bladed rotor is the most efficient design, and a single windmill has the best extraction efficiency, multiple blades (usually 3, but 2 is reasonably common in smaller machines (even though it suffers from 'tower thump'), and there are some experimental large machines using only 1 blade), terrain details, local variations in wind consistency, wind shear and a whole bunch of other factors including humidity and so on play havoc with any simple 'back of the envelope' calculations.
A 7 meter per second wind in the desert versus a 7 meter per second wind at sea level can make a huge difference.
If you really want to dig in to this I'd advise you to go and read the http://www.awea.org/ site as well as a community for homebrew wind enthousiasts called fieldlines (http://www.fieldlines.com/), I used to be an active member of the second but since I've left Canada I have not worked on anything renewable energy related.
I spent a good 2 years studying this stuff before being able to make a very small machine, the forces involved in even such a 'toy' (2.4 KW) machine are very impressive and the amount of knowledge you need to pull it off was far beyond what I ever had expected.
Windmills for power generation are right at the crossroads between many different disciplines, including aerodynamics, magnetics, electrical theory, semiconductors and structural engineering, coupled with a very powerful and unpredictable adversary, the wind.
If anything that journey taught me great respect for the people that design those large machines and one the whole get it right most of the time.
The practical upshot of that is that you can't slow the air down to a standstill, and hence you can only extract so much power.
The next step is the difference between the theoretical maximum and the actual rotor used to extract the energy, this will always be a compromise, but real world rotor efficiencies of about 50% can be reached. Then there's the generator/alternator (depending on the type of machine) losses and gearbox losses if a gearbox is used (there are very large direct drive models, specifically the Enercon series).
After all is said and done figure about 35 to 48% of the wind 'input' energy can be extracted and applied to do something useful, assuming the wind is blowing at 'rated speed' (when the machine produces its maximum design power).
If the wind goes over that speed you will lose power because the blades will be 'furled' to take them out of the wind to limit the rotor speed to something safe, and to avoid burning up the powertrain or wrecking the gearbox.
Then there are still transmission losses but we can leave those out because they apply to any power source connected to the grid.
Typical rotor diameters for 2MW machines are in the 80 to 90 meter range depending on how efficient the machine is.
There is no 'typical wind farm', it all depends on the effects of the terrain and the windmills on each other and the amount of investment.
A single bladed rotor is the most efficient design, and a single windmill has the best extraction efficiency, multiple blades (usually 3, but 2 is reasonably common in smaller machines (even though it suffers from 'tower thump'), and there are some experimental large machines using only 1 blade), terrain details, local variations in wind consistency, wind shear and a whole bunch of other factors including humidity and so on play havoc with any simple 'back of the envelope' calculations.
A 7 meter per second wind in the desert versus a 7 meter per second wind at sea level can make a huge difference.
If you really want to dig in to this I'd advise you to go and read the http://www.awea.org/ site as well as a community for homebrew wind enthousiasts called fieldlines (http://www.fieldlines.com/), I used to be an active member of the second but since I've left Canada I have not worked on anything renewable energy related.
I spent a good 2 years studying this stuff before being able to make a very small machine, the forces involved in even such a 'toy' (2.4 KW) machine are very impressive and the amount of knowledge you need to pull it off was far beyond what I ever had expected.
Windmills for power generation are right at the crossroads between many different disciplines, including aerodynamics, magnetics, electrical theory, semiconductors and structural engineering, coupled with a very powerful and unpredictable adversary, the wind.
If anything that journey taught me great respect for the people that design those large machines and one the whole get it right most of the time.
When they mess up it looks like this:
http://home.wxs.nl/~hzwarber/wind/plaatjes/crash_turm2.jpg